Either donor or contributor is suitable for someone who gives money to a charity, but a donation is generally understood to be a gift, whether of funds or some possession of value, whereas a contribution is anything that assists in the effort, including skills, knowledge, connections, or volunteer labor. (Donator is uncommon.)
As such, a donor is almost always one who has made a donation of funds or marketable goods and services, e.g. one donor gave 500 shares of stock, another gave 50 hours of accounting, another a brochure design worth $500. All of those people could also be called contributors, but that term could include people who volunteer their time or talent.
An organization may wish to thank its contributors as a more inclusive term, covering those who dedicate effort as well as money. In other cases, though, they may simply use contributor and contribution as direct synonyms to avoid donor and donation— I do detect a slight aversion in the U.S. to the latter, perhaps because we are subjected to so many appeals and are thus prone to charity exhaustion With our donation— sorry, gift or contribution— the museum, hospital, or university will rank us as a supporter, sponsor, benefactor, or patron.